​Locus

About Geometry Worksheet Assignment 2.21:     

 

Assignment 2.21 is an introduction to locus of points in a plane.

 

Prerequisite Skills:  Identify parallel lines (Assignment 1.6).  Identify angle bisectors (Assignment 2.15).  Identify perpendicular lines (Assignment 2.16).  Identify perpendicular bisectors (Assignment 2.17)

 

Definition:  A locus is the set of all points that satisfy a given condition.

 

Theorems:  In a plane, the locus of points at a fixed distance from a given point is a circle.

 

                         In a plane, the locus of points at a fixed distance from a line is a pair of parallel lines.

 

                        In a plane, the locus of points equidistant from two given points is the perpendicular bisector of the line segment between the points.

 

                        In a plane, the locus of points equidistant from parallel lines is a line parallel to each line at the same distance from esch line.

 

                        In a plane, the locus of points equidistant from the sides of a angle is the bisector of the angle.